Welcome to ETO.
There isn't really a housing. There are the dark laminations which are the steel bits that make up most of the weight of the transformer, and a silver coloured clamp that goes around the lamination. You should just take the earth wire to the clamp. If it's in a metal box, and the metal box is earthed, then the that's all you need to do.
If there's no way of making contact with the laminations or the clamp, for instance if it's in a plastic box and there aren't any metal bits that can be touched, you don't really need the earth at all.
You need to connect live and neutral to the outer two pins labelled 115 V, and join together the inner two. It is a good idea to cover all of those connections so that loose wires that are supposed to be low voltage can't touch the live, or neutral or the wire between the two inner terminals. That sort of fault is far more likely than the transformer failing to isolate the mains.
You can also earth the outputs at some point. If you've got rectifiers and some sort of regulator connected to the windings, than you would normally earth one side of the output of the regulator, often the negative. However, there is no problem running it without an earth. A transformer from RS will provide good isolation from the mains, but earthing the output will stop you getting a shock if there is a loose wire that touches something live.
Instead of that transformer, there is a slightly cheaper, lighter and easier to use alternative, a toroidal transformer.
https://uk.rs-online.com/web/p/toroidal-transformers/6718952/
Just stick a mains plug on the brown and blue wires, and it's working and safe. Ok, if you short it's output out, it will overheat in a couple of minutes. But on the mains safety, there are no exposed metal bits.
The only danger for the unwary on toroidals is when mounting them, you must not put anything conductive through the middle that loops back around the outside. So a mounting bolt onto a metal box is fine, as long as the top of the box (or anything else conductive) does not touch the bolt head or the metal plate that is part of the mounting kit. There will only be a tiny voltage, probably less than 1/4 of a Volt, but if there is a conductive path, quite a lot of current will flow.